NetSci 2016 - Diffusion and Transport
Thursday, June 2, 2016 / 16:10-17:50 / Dongkang C, Avenue 3F
Wei Chien Benny Chin, Tzai Hung Wen, and Pei Chun Lai (National Taiwan University, Taiwan)
The aim of this study is to understand
the network characteristics that influence the occurance of
traffic congestion.
two components:
imagine,
the streets are connected to each other, and
there are lots of cars moving on
the streets...
When a car is moving on a street, it moves along the street.
When it comes to an intersection, it might keep moving straight, or take a turn to the left/right.
At first,
lets just assume that the turning probabilities to the different directions are equal.

canvas = toyplot.Canvas(450, 450)
axes = canvas.cartesian()
line = axes.plot(lx,ly, style={"stroke":"steelblue", "stroke-width":10})
line = axes.plot(ly,lx, style={"stroke":"steelblue", "stroke-width":5})
mark = axes.scatterplot(x, y, size=20, marker='s')
canvas.animate(len(x) + 1, callback)
expanded the simple model with the real street network (of Taipei City)
from IPython.display import HTML
HTML('<iframe src="https://player.vimeo.com/video/168713881" width="640"\
height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen \
allowfullscreen></iframe><p><a href="https://vimeo.com/168713881">\
simulation - moving cars on streets taking turn randomly - v0.2</a>\
from <a href="https://vimeo.com/user11082431">Benny Chin</a> on \
<a href="https://vimeo.com">Vimeo</a>.</p>')
this model is similar to the concept behind Google's PageRank (PR) algorithm.
PageRank uses a random move model (the random surfer),
and analyzes the hyperlink connectivity,
namely the referencing network,
to identify the key webpages.
"which pages are referenced more than others."
basic-form: PageRank (Brin & Page, 1998)
$ PR_{t}(i) = \sum_{j\in IN(i)} PR_{t-1}(j) \times \frac{1}{outdeg(j)} $
$ IN(i) $: the incoming node set of i; $ outdeg(j) $: the out-degree of j.

Therefore,
we can run the PageRank on the street network,
to identify the important street segment where there are lots of cars would pass by.
The output of PageRank, the score of each street, could be used to represent how important the street is.
the movements of cars are not completely random in the real world.

Most of the cars will move along the main direction (keep moving straight).
to capture this concept in the model,
we introduce the "attractiveness" ($attr$) of street segment.
$ attr =$ a composite variable that differentiate the streets by their ability to attract cars.
turning probability:
$ turning = \frac{attr(i)}{\sum_{k\in OUT(j)}attr(k)} $
but, how do we know the distribution of the attractiveness?
the modified PR: Flow-based PageRank (FBPR):
$ FBPR_{t}(i) = \sum_{j\in IN(i)} FBPR_{t-1}(j) \times turning $
canvas = toyplot.Canvas(450, 450)
axes = canvas.cartesian()
line = axes.plot(lx,ly, style={"stroke":"steelblue", "stroke-width":10})
line = axes.plot(ly,lx, style={"stroke":"steelblue", "stroke-width":5})
mark = axes.scatterplot(x2, y2, size=20, marker='s')
canvas.animate(len(x2) + 1, callback)
While
the turning probability could be calculated from the calibrated attractiveness,
we could measure
$ entropy(j) = -\sum_{k \in OUT(j)} (turning(j,k) \times ln(turning(j,k))) $
the entropy of the turning probabilities origin from the street.

in summary,
the everyday problem for most of the cities in the world.
In most developing countries, the capacity of streets do not meet the rising number of car owners, hence the congestion problem become more serious.

(apart from unexpected factors, e.g. accidents)
Traffic congestion happens while
lots of people go to the same destinations (works, schools) at the same time, putting huge pressure on the street network.
on rush hours
in order to analyze the connectivity of streets, and to measure the demands and design of each street
we propose the Flow-based PageRank.


the ability of streets for bringing people to their destination.

the potential number of vehicles passing by the street?
the vehicle detector (VD) data: the real traffic volume data

is the network structure too complex?
#from IPython.display import HTML
HTML('<iframe src="https://player.vimeo.com/video/168714357" width="640"\
height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen \
allowfullscreen></iframe><p><a href="https://vimeo.com/168714357">\
simulation - moving cars on streets turning with the estimated probability\
- v0.2</a> from <a href="https://vimeo.com/user11082431">Benny Chin</a>\
on <a href="https://vimeo.com">Vimeo</a>.</p>')



Is the design of the street network meant to be easily get into congestion?
if lots of cars started moving at the same times,
will the city become congested easily?
Where are the cars concentrated?
Where will the cars turn?
my contact info:
Benny Chin,
wcchin.88@gmail.com
a Ph.D. student at National Taiwan University.
links: